I'm too lazy to deal with some other spec on a healer. As most probably it would be heal for PvP and heal for PvE, so that's why not that fond of leveling a healer in DPS spec.

Instant heals are good and if paladin can do that I might lean towards that class. I was thinking of disc priest, but I've tried that in the end of cata, wasn't really fun play (not to me at least). I won't make a new druid (as I already have one as tank/DPS (I'm that kind of nutcase that would like to have 11 different classes on one faction in a same server).

Paladin. Holy shock, judgment and denounce are good for dealing damage if you need to. Fast dungeon queued, carrying your team to BG wins, etc always helps. Also as a paladin you can always equip any int/spirit gear if need be for the upgrade, priest you're limited to cloth.

That depends on if you're talking about pvp while leveling or pvp at 90.

Mistweaver monks and discipline priests can both dps fairly well for leveling, however I don't believe that either of their level 90 pvp states is all that good at the moment. Healing classes that are better at level 90 pvp right now (shamans and pallies, which are both pretty much always good for pvp) probably wouldn't be quite as easy to level in healing specs.

Pre-90 pvp probably doesn't matter as much because none of it is balanced in the least bit, and at the bottom of the bracket it doesn't matter what class you are you'll get owned by the people at the top of the bracket.

It depends on the type of pvp you want to do also. For BGs there is less difference (healers are so few that you will find yourself useful regardless), though I prefer Disc Priest or Shammy. If you want to do Arena there's a lot less forgiveness for playing badly, and playing badly depends a lot on how well you can learn the mechanics of the class. I would suggest doing a thorough look at the current arena strats and figure out how the mechanics work. You may find that a class you have liked is really boring in arena vs bgs. Just do your homework and you'll find out what will suit you best.

Favorite/easiest healer for me to level was a disc priest because of the damage you can unleash which actually heals:

"Each time you deal damage with Smite, Holy Fire, and Penance, the lowest health player within 40 yards of the target (the target you have dealt damage to) is healed for the amount of damage that you did."